Disentangling subpopulations in single-molecule FRET and ALEX experiments with photon distribution analysis

Among the advantages of the single-molecule approach when used to study biomolecular structural dynamics and interaction is its ability to distinguish between and independently observe minor subpopulations. In a single-molecule Förster resonance energy transfer (FRET) and alternating laser excitation diffusion experiment, the various populations are apparent in the resultant histograms. However, because histograms are calculated based on the per-burst mean FRET and stoichiometry ratio and not on the internal photon distribution, much of the acquired information is lost, thereby reducing the capabilities of the method. Here we suggest what to our knowledge is a novel statistical analysis tool that significantly enhances these capabilities, and we use it to identify and isolate static and dynamic subpopulations. Based on a kernel density estimator and a proper photon distribution analysis, for each individual burst, we calculate scores that reflect properties of interest. Specifically, we determine the FRET efficiency and brightness ratio distributions and use them to reveal 1), the underlying structure of a two-state DNA-hairpin and a DNA hairpin that is bound to DNA origami; 2), a minor doubly labeled dsDNA subpopulation concealed in a larger singly labeled dsDNA; and 3), functioning DNA origami motors concealed within a larger subpopulation of defective motors. Altogether, these findings demonstrate the usefulness of the proposed approach. The method was developed and tested using simulations, its rationality is described, and a computer algorithm is provided.     

Histone H3 Tail Modifications Alter Structure and Dynamics of the H1 C-Terminal Domain Within Nucleosomes

The highly positively charged and intrinsically disordered H1 C-terminal domain (CTD) undergoes extensive condensation upon binding to nucleosomes, and stabilizes nucleosomes and higher-order chromatin structures but its interactions in chromatin are not well defined. Using single-molecule FRET we found that about half of the H1 CTDs in H1-nucleosome complexes exhibit well-defined FRET values indicative of distinct, static conformations, while the remainder of the population exhibits exchange between multiple defined FRET structures. Moreover, crosslinking studies indicate that the first 30 residues of the H1 CTD participate in relatively localized contacts with the first ∼25 bp of linker DNA, and that two separate regions in the CTD contribute to H1-dependent organization of linker DNA. Finally, we show that acetylation mimetics within the histone H3 tail markedly reduce the overall extent of H1 CTD condensation and significantly increase the fraction of H1 CTDs undergoing dynamic exchange between FRET states. Our results indicate the nucleosome-bound H1 CTD adopts loosely defined structures that exhibit significantly enhanced dynamics and decondensation upon epigenetic acetylation within the H3 tail.     

Multimodal Measurements of Single-Molecule Dynamics Using FluoRBT

Single-molecule methods provide direct measurements of macromolecular dynamics, but are limited by the number of degrees of freedom that can be followed at one time. High-resolution rotor bead tracking (RBT) measures DNA torque, twist, and extension, and can be used to characterize the structural dynamics of DNA and diverse nucleoprotein complexes. Here, we extend RBT to enable simultaneous monitoring of additional degrees of freedom. Fluorescence-RBT (FluoRBT) combines magnetic tweezers, infrared evanescent scattering, and single-molecule FRET imaging, providing real-time multiparameter measurements of complex molecular processes. We demonstrate the capabilities of FluoRBT by conducting simultaneous measurements of extension and FRET during opening and closing of a DNA hairpin under tension, and by observing simultaneous changes in FRET and torque during a transition between right-handed B-form and left-handed Z-form DNA under controlled supercoiling. We discover unanticipated continuous changes in FRET with applied torque, and also show how FluoRBT can facilitate high-resolution FRET measurements of molecular states, by using a mechanical signal as an independent temporal reference for aligning and averaging noisy fluorescence data. By combining mechanical measurements of global DNA deformations with FRET measurements of local conformational changes, FluoRBT will enable multidimensional investigations of systems ranging from DNA structures to large macromolecular machines.     

Unraveling secrets of telomeres: One molecule at a time

Telomeres play important roles in maintaining the stability of linear chromosomes. Telomere maintenance involves dynamic actions of multiple proteins interacting with long repetitive sequences and complex dynamic DNA structures, such as G-quadruplexes, T-loops and t-circles. Given the heterogeneity and complexity of telomeres, single-molecule approaches are essential to fully understand the structure–function relationships that govern telomere maintenance. In this review, we present a brief overview of the principles of single-molecule imaging and manipulation techniques. We then highlight results obtained from applying these single-molecule techniques for studying structure, dynamics and functions of G-quadruplexes, telomerase, and shelterin proteins.     

Single-molecule fluorescence resonance energy transfer

Fluorescent resonance energy transfer (FRET) is a powerful technique for studying conformational distribution and dynamics of biological molecules. Some conformational changes are difficult to synchronize or too rare to detect using ensemble FRET. FRET, detected at the single-molecule level, opens up new opportunities to probe the detailed kinetics of structural changes without the need for synchronization. Here, we discuss practical considerations for its implementation including experimental apparatus, fluorescent probe selection, surface immobilization, single-molecule FRET analysis schemes, and interpretation.     

Optimizing Methods to Recover Absolute FRET Efficiency from Immobilized Single Molecules

Microscopy-based fluorescence resonance energy transfer (FRET) experiments measure donor and acceptor intensities by isolating these signals with a series of optical elements. Because this filtering discards portions of the spectrum, the observed FRET efficiency is dependent on the set of filters in use. Similarly, observed FRET efficiency is also affected by differences in fluorophore quantum yield. Recovering the absolute FRET efficiency requires normalization for these effects to account for differences between the donor and acceptor fluorophores in their quantum yield and detection efficiency. Without this correction, FRET is consistent across multiple experiments only if the photophysical and instrument properties remain unchanged. Here we present what is, to our knowledge, the first systematic study of methods to recover the true FRET efficiency using DNA rulers with known fluorophore separations. We varied optical elements to purposefully alter observed FRET and examined protein samples to achieve quantum yields distinct from those in the DNA samples. Correction for calculated instrument transmission reduced FRET deviations, which can facilitate comparison of results from different instruments. Empirical normalization was more effective but required significant effort. Normalization based on single-molecule photobleaching was the most effective depending on how it is applied. Surprisingly, per-molecule γ-normalization reduced the peak width in the DNA FRET distribution because anomalous γ-values correspond to FRET outliers. Thus, molecule-to-molecule variation in gamma has an unrecognized effect on the FRET distribution that must be considered to extract information on sample dynamics from the distribution width.     

FRETmatrix: a general methodology for the simulation and analysis of FRET in nucleic acids

Förster resonance energy transfer (FRET) is a technique commonly used to unravel the structure and conformational changes of biomolecules being vital for all living organisms. Typically, FRET is performed using dyes attached externally to nucleic acids through a linker that complicates quantitative interpretation of experiments because of dye diffusion and reorientation. Here, we report a versatile, general methodology for the simulation and analysis of FRET in nucleic acids, and demonstrate its particular power for modelling FRET between probes possessing limited diffusional and rotational freedom, such as our recently developed nucleobase analogue FRET pairs (base–base FRET). These probes are positioned inside the DNA/RNA structures as a replacement for one of the natural bases, thus, providing unique control of their position and orientation and the advantage of reporting from inside sites of interest. In demonstration studies, not requiring molecular dynamics modelling, we obtain previously inaccessible insight into the orientation and nanosecond dynamics of the bases inside double-stranded DNA, and we reconstruct high resolution 3D structures of kinked DNA. The reported methodology is accompanied by a freely available software package, FRETmatrix, for the design and analysis of FRET in nucleic acid containing systems.     

Similarity Measures for Protein Ensembles

Analyses of similarities and changes in protein conformation can provide important information regarding protein function and evolution. Many scores, including the commonly used root mean square deviation, have therefore been developed to quantify the similarities of different protein conformations. However, instead of examining individual conformations it is in many cases more relevant to analyse ensembles of conformations that have been obtained either through experiments or from methods such as molecular dynamics simulations. We here present three approaches that can be used to compare conformational ensembles in the same way as the root mean square deviation is used to compare individual pairs of structures. The methods are based on the estimation of the probability distributions underlying the ensembles and subsequent comparison of these distributions. We first validate the methods using a synthetic example from molecular dynamics simulations. We then apply the algorithms to revisit the problem of ensemble averaging during structure determination of proteins, and find that an ensemble refinement method is able to recover the correct distribution of conformations better than standard single-molecule refinement.     

Single-molecule FRET of protein structure and dynamics - a primer

Single-molecule spectroscopy has developed into a widely used method for probing the structure, dynamics, and mechanisms of biomolecular systems, especially in combination with Förster resonance energy transfer (FRET). In this introductory tutorial, essential concepts and methods will be outlined, from the FRET process and the basic considerations for sample preparation and instrumentation to some key elements of data analysis and photon statistics. Different approaches for obtaining dynamic information over a wide range of timescales will be explained and illustrated with examples, including the quantitative analysis of FRET efficiency histograms, correlation spectroscopy, fluorescence trajectories, and microfluidic mixing.     

Static and dynamic expression of life history traits in the northern fulmar Fulmarus glacialis

Understanding the static and dynamic expression of life history traits is a prerequisite for the development of a causal theory of the evolution of aging and of life histories. We analyzed the statics and dynamics of reproduction and survival in a wild population of the northern fulmar, Fulmarus glacialis (Procellaridae). Survival rate is most influenced by year as compared to age and cohort. When temporal variation is ignored, survival rate increases slowly with age and then declines more rapidly at late ages. Survival rate contingent upon reproductive ‘stratum’ (producing an egg, hatching an egg, fledging a hatchling) also exhibits this pattern. Survival and reproduction have a positive static association in that survival rate increases as the apparent energy allocated to reproduction increases (as indexed by stratum). There is a broad distribution of realized lifetime reproductive success, which could be due to ‘fixed’ heterogeneity, with some individuals always having low survival and reproduction and others always having high survival and reproduction, or be due to ‘dynamic’ heterogeneity, with all individuals having the same expected reproductive and survival rates. Analysis of stochastic stratum dynamics indicates that individuals do not remain long in any given stratum and suggest that the variation among individuals with respect to lifetime reproductive success is due to dynamic heterogeneity. The probability of producing an egg increases with age for both sexes, whereas the probability of producing a fledgling initially declines with age and then increases. These results underscore the necessity of understanding the static and dynamic expression of demographic traits when making a causal claim about their evolution.     

A comparison of Förster resonance energy transfer analysis approaches for Nanodrop fluorometry

Ensemble Förster resonance energy transfer (FRET) results can be analyzed in a variety of ways. Due to experimental artifacts, the results obtained from different analysis approaches are not always the same. To determine the optimal analysis approach to use for Nanodrop fluorometry, we have performed both ensemble and single-molecule FRET studies on oligomers of double-stranded DNA. We compared the single-molecule FRET results with those obtained using various ensemble FRET analysis approaches. This comparison shows that for Nanodrop fluorometry, analyzing the increase of the acceptor fluorescence is less likely to introduce errors in estimates of FRET efficiencies compared with analyzing the fluorescence intensity of the donor in the absence and presence of the acceptor.     

Real-time single-molecule studies of the motions of DNA polymerase fingers illuminate DNA synthesis mechanisms

DNA polymerases maintain genomic integrity by copying DNA with high fidelity. A conformational change important for fidelity is the motion of the polymerase fingers subdomain from an open to a closed conformation upon binding of a complementary nucleotide. We previously employed intra-protein single-molecule FRET on diffusing molecules to observe fingers conformations in polymerase–DNA complexes. Here, we used the same FRET ruler on surface-immobilized complexes to observe fingers-opening and closing of individual polymerase molecules in real time. Our results revealed the presence of intrinsic dynamics in the binary complex, characterized by slow fingers-closing and fast fingers-opening. When binary complexes were incubated with increasing concentrations of complementary nucleotide, the fingers-closing rate increased, strongly supporting an induced-fit model for nucleotide recognition. Meanwhile, the opening rate in ternary complexes with complementary nucleotide was 6 s⁻¹, much slower than either fingers closing or the rate-limiting step in the forward direction; this rate balance ensures that, after nucleotide binding and fingers-closing, nucleotide incorporation is overwhelmingly likely to occur. Our results for ternary complexes with a non-complementary dNTP confirmed the presence of a state corresponding to partially closed fingers and suggested a radically different rate balance regarding fingers transitions, which allows polymerase to achieve high fidelity.     

Quantitative time domain analysis of lifetime‐based Förster resonant energy transfer measurements with fluorescent proteins: Static random isotropic fluorophore orientation distributions

Förster resonant energy transfer (FRET) measurements are widely used to obtain information about molecular interactions and conformations through the dependence of FRET efficiency on the proximity of donor and acceptor fluorophores. Fluorescence lifetime measurements can provide quantitative analysis of FRET efficiency and interacting population fraction. Many FRET experiments exploit the highly specific labelling of genetically expressed fluorescent proteins, applicable in live cells and organisms. Unfortunately, the typical assumption of fast randomization of fluorophore orientations in the analysis of fluorescence lifetime‐based FRET readouts is not valid for fluorescent proteins due to their slow rotational mobility compared to their upper state lifetime. Here, previous analysis of effectively static isotropic distributions of fluorophore dipoles on FRET measurements is incorporated into new software for fitting donor emission decay profiles. Calculated FRET parameters, including molar population fractions, are compared for the analysis of simulated and experimental FRET data under the assumption of static and dynamic fluorophores and the intermediate regimes between fully dynamic and static fluorophores, and mixtures within FRET pairs, is explored. Finally, a method to correct the artefact resulting from fitting the emission from static FRET pairs with isotropic angular distributions to the (incorrect) typically assumed dynamic FRET decay model is presented.      

Conformational dynamics of full-length inducible human Hsp70 derived from microsecond molecular dynamics simulations in explicit solvent

Human 70?kDa heat shock protein (hHsp70) is an ATP-dependent chaperone and is currently an important target for developing new drugs in cancer therapy. Knowledge of the conformations of hHsp70 is central to understand the interactions between its nucleotide-binding domain (NBD) and substrate-binding domain (SBD) and is a prerequisite to design inhibitors. The conformations of ADP-bound (or nucleotide-free) hHsp70 and ATP-bound hHsp70 was investigated by using unbiased all-atom molecular dynamics (MD) simulations of homology models of hHsp70 in explicit solvent on a timescale of .5 and 2.7 μs, respectively. The conformational heterogeneity of hHsp70 was analyzed by computing effective free-energy landscapes (FELs) and distance distribution between selected pair of residues. These theoretical data were compared with those extracted from single-molecule Förster resonance energy transfer (FRET) experiments and to small-angle X-ray scattering (SAXS) data of Hsp70 homologs. The distance between a pair of residues in FRET is systematically larger than the distance computed in MD which is interpreted as an effect of the size and of the dynamics of the fluorescent probes. The origin of the conformational heterogeneity of hHsp70 in the ATP-bound state is due to different binding modes of the helix B of the SBD onto the NBD. In the ADP-bound (or nucleotide-free) state, it arises from the different closed conformations of the SBD and from the different positions of the SBD relative to the NBD. In each nucleotide-binding state, Hsp70 is better represented by an ensemble of conformations on a μs timescale corresponding to different local minima of the FEL.

An animated interactive 3D complement (I3DC) is available in Proteopedia at http://proteopedia.org/w/Journal:JBSD:30     

Conformational states and fluctuations in endothelial nitric oxide synthase under calmodulin regulation

Mechanisms that regulate nitric oxide synthase enzymes (NOS) are of interest in biology and medicine. Although NOS catalysis relies on domain motions and is activated by calmodulin (CaM) binding, the relationships are unclear. We used single-molecule fluorescence resonance energy transfer (FRET) spectroscopy to elucidate the conformational states distribution and associated conformational fluctuation dynamics of the two NOS electron transfer domains in an FRET dye-labeled endothelial NOS reductase domain (eNOSr) and to understand how CaM affects the dynamics to regulate catalysis by shaping the spatial and temporal conformational behaviors of eNOSr. In addition, we developed and applied a new imaging approach capable of recording three-dimensional FRET efficiency versus time images to characterize the impact on dynamic conformal states of the eNOSr enzyme by the binding of CaM, which identifies clearly that CaM binding generates an extra new open state of eNOSr, resolving more detailed NOS conformational states and their fluctuation dynamics. We identified a new output state that has an extra open conformation that is only populated in the CaM-bound eNOSr. This may reveal the critical role of CaM in triggering NOS activity as it gives conformational flexibility for eNOSr to assume the electron transfer output FMN-heme state. Our results provide a dynamic link to recently reported EM static structure analyses and demonstrate a capable approach in probing and simultaneously analyzing all of the conformational states, their fluctuations, and the fluctuation dynamics for understanding the mechanism of NOS electron transfer, involving electron transfer among FAD, FMN, and heme domains, during nitric oxide synthesis.     

Poly(A)-targeting molecular beacons: Fluorescence resonance energy transfer-based in vitro quantitation and time-dependent imaging in live cells

Quantitation of poly(A)-RNA, time-dependent visualization of intracellular poly(A)(+)-RNA localization in living mammalian cells, and time-resolved intracellular binding dynamics of molecular beacons at the single-molecule level using a fluorescence resonance energy transfer (FRET)-based molecular beacon are described. FRET-based molecular beacons were designed as poly(A)-targeting probes to be oligonucleotides that contained Cy5 and Cy3 fluorescent dyes at the strand ends and a poly(A)-targeting sequence inside the strand. Our ratiometric analysis using poly(A)-targeting probes allowed for highly specific and wide-ranging detection (from 1.25nM to 0.5μM) of poly(A)-RNA, as well as for determination of K(d) values, and revealed a distribution of the probe itself and localization of the target RNA sequence in cells. Furthermore, time-dependent FRET-mediated fluorescence changes at the single-molecule level caused by the folding-induced gradual conformation changes in live cells were observed.     

Highly Disordered Amyloid-β Monomer Probed by Single-Molecule FRET and MD Simulation

Monomers of amyloid-β (Aβ) protein are known to be disordered, but there is considerable controversy over the existence of residual or transient conformations that can potentially promote oligomerization and fibril formation. We employed single-molecule Förster resonance energy transfer (FRET) spectroscopy with site-specific dye labeling using an unnatural amino acid and molecular dynamics simulations to investigate conformations and dynamics of Aβ isoforms with 40 (Aβ40) and 42 residues (Aβ42). The FRET efficiency distributions of both proteins measured in phosphate-buffered saline at room temperature show a single peak with very similar FRET efficiencies, indicating there is apparently only one state. 2D FRET efficiency-donor lifetime analysis reveals, however, that there is a broad distribution of rapidly interconverting conformations. Using nanosecond fluorescence correlation spectroscopy, we measured the timescale of the fluctuations between these conformations to be ～35 ns, similar to that of disordered proteins. These results suggest that both Aβ40 and Aβ42 populate an ensemble of rapidly reconfiguring unfolded states, with no long-lived conformational state distinguishable from that of the disordered ensemble. To gain molecular-level insights into these observations, we performed molecular dynamics simulations with a force field optimized to describe disordered proteins. We find, as in experiments, that both peptides populate configurations consistent with random polymer chains, with the vast majority of conformations lacking significant secondary structure, giving rise to very similar ensemble-averaged FRET efficiencies.     

Analysis of single-molecule FRET trajectories using hidden Markov modeling

The analysis of single-molecule fluorescence resonance energy transfer (FRET) trajectories has become one of significant biophysical interest. In deducing the transition rates between various states of a system for time-binned data, researchers have relied on simple, but often arbitrary methods of extracting rates from FRET trajectories. Although these methods have proven satisfactory in cases of well-separated, low-noise, two- or three-state systems, they become less reliable when applied to a system of greater complexity. We have developed an analysis scheme that casts single-molecule time-binned FRET trajectories as hidden Markov processes, allowing one to determine, based on probability alone, the most likely FRET-value distributions of states and their interconversion rates while simultaneously determining the most likely time sequence of underlying states for each trajectory. Together with a transition density plot and Bayesian information criterion we can also determine the number of different states present in a system in addition to the state-to-state transition probabilities. Here we present the algorithm and test its limitations with various simulated data and previously reported Holliday junction data. The algorithm is then applied to the analysis of the binding and dissociation of three RecA monomers on a DNA construct.